A surgical obturator adapted to penetrate a body wall includes an elongate shaft having an axis which extends between a proximal end and a distal end. A bladeless tip, disposed at the distal end of the shaft has an outer surface which extends to a blunt point. The outer surface has a pair of side sections separated by an intermediate section. The side sections extend from the blunt point radially outwardly with progressive positions proximally along the axis. These side sections include a distal portion in proximity to the blunt point, and a proximal portion in proximity to the shaft. The distal portion of the side section is twisted radially with respect to the proximal portion of the side section. The outer surface in radial cross section has the general configuration of a geometric shape which rotates in a first direction about the axis with progressive proximal radial cross sections along the axis.